algebra-math-problems-algebra-practice-learning-printable-college - Free Printable
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Step-by-step solution for: algebra-math-problems-algebra-practice-learning-printable-college
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Show Answer Key & Explanations
Step-by-step solution for: algebra-math-problems-algebra-practice-learning-printable-college
Here are the step-by-step solutions for each problem on the worksheet.
1. $(-9)^2 + 3^4$
* First, calculate $(-9)^2$. A negative number squared becomes positive: $-9 \times -9 = 81$.
* Next, calculate $3^4$. This is $3 \times 3 \times 3 \times 3$.
* $3 \times 3 = 9$
* $9 \times 3 = 27$
* $27 \times 3 = 81$
* Add them together: $81 + 81 = 162$.
2. $(-9)^{-2} + (-7)^{-2}$
* Negative exponents mean you take the reciprocal (flip the fraction). The rule is $x^{-n} = \frac{1}{x^n}$.
* $(-9)^{-2} = \frac{1}{(-9)^2} = \frac{1}{81}$.
* $(-7)^{-2} = \frac{1}{(-7)^2} = \frac{1}{49}$.
* To add $\frac{1}{81} + \frac{1}{49}$, find a common denominator. Since 81 and 49 share no common factors, multiply them: $81 \times 49 = 3969$.
* Convert fractions:
* $\frac{1 \times 49}{3969} = \frac{49}{3969}$
* $\frac{1 \times 81}{3969} = \frac{81}{3969}$
* Add numerators: $49 + 81 = 130$.
* Result: $\frac{130}{3969}$.
3. $10^{-3} + (-9)^2$
* $10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001$.
* $(-9)^2 = -9 \times -9 = 81$.
* Add them: $81 + 0.001 = 81.001$.
4. $9^{-3} + (-9)^0$
* $9^{-3} = \frac{1}{9^3}$. Calculate $9^3$: $9 \times 9 = 81$, and $81 \times 9 = 729$. So, $\frac{1}{729}$.
* Any non-zero number to the power of 0 is 1. So, $(-9)^0 = 1$.
* Add them: $1 + \frac{1}{729} = 1 \frac{1}{729}$ (or $\frac{730}{729}$).
5. $4^{-2} + (-6)^3$
* $4^{-2} = \frac{1}{4^2} = \frac{1}{16}$.
* $(-6)^3 = -6 \times -6 \times -6$.
* $-6 \times -6 = 36$
* $36 \times -6 = -216$
* Add them: $\frac{1}{16} + (-216) = -216 + \frac{1}{16}$.
* As a mixed number: $-215 \frac{15}{16}$ (since you are adding a small positive fraction to a large negative integer, it moves slightly closer to zero).
* As an improper fraction: $-216 = -\frac{3456}{16}$. Then $-\frac{3456}{16} + \frac{1}{16} = -\frac{3455}{16}$.
6. $-9^2 + 3^3$
* Careful here: There are no parentheses around the 9 in $-9^2$. This means you square the 9 first, then apply the negative sign.
* $9^2 = 81$, so $-9^2 = -81$.
* $3^3 = 3 \times 3 \times 3 = 27$.
* Add them: $-81 + 27 = -54$.
7. $4^0 + 8^0$
* Any non-zero number to the power of 0 is 1.
* $4^0 = 1$.
* $8^0 = 1$.
* Add them: $1 + 1 = 2$.
8. $-3^0 + (-8)^2$
* $-3^0$: Again, no parentheses around the 3. $3^0 = 1$, so $-3^0 = -1$.
* $(-8)^2$: Parentheses mean the negative is included. $-8 \times -8 = 64$.
* Add them: $-1 + 64 = 63$.
9. $8^4 + 2^{-3}$
* $8^4 = 8 \times 8 \times 8 \times 8$.
* $8 \times 8 = 64$
* $64 \times 8 = 512$
* $512 \times 8 = 4096$
* $2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$.
* Add them: $4096 + 0.125 = 4096.125$.
10. $(-2)^4 + (-0.02)^3$
* $(-2)^4 = -2 \times -2 \times -2 \times -2$.
* $(-2 \times -2) = 4$
* $(4 \times -2) = -8$
* $(-8 \times -2) = 16$
* $(-0.02)^3 = -0.02 \times -0.02 \times -0.02$.
* $0.02 \times 0.02 = 0.0004$
* $0.0004 \times -0.02 = -0.000008$
* Add them: $16 + (-0.000008) = 15.999992$.
Final Answer:
1. 162
2. 130/3969
3. 81.001
4. 730/729 (or 1 1/729)
5. -3455/16 (or -215 15/16)
6. -54
7. 2
8. 63
9. 4096.125
10. 15.999992
1. $(-9)^2 + 3^4$
* First, calculate $(-9)^2$. A negative number squared becomes positive: $-9 \times -9 = 81$.
* Next, calculate $3^4$. This is $3 \times 3 \times 3 \times 3$.
* $3 \times 3 = 9$
* $9 \times 3 = 27$
* $27 \times 3 = 81$
* Add them together: $81 + 81 = 162$.
2. $(-9)^{-2} + (-7)^{-2}$
* Negative exponents mean you take the reciprocal (flip the fraction). The rule is $x^{-n} = \frac{1}{x^n}$.
* $(-9)^{-2} = \frac{1}{(-9)^2} = \frac{1}{81}$.
* $(-7)^{-2} = \frac{1}{(-7)^2} = \frac{1}{49}$.
* To add $\frac{1}{81} + \frac{1}{49}$, find a common denominator. Since 81 and 49 share no common factors, multiply them: $81 \times 49 = 3969$.
* Convert fractions:
* $\frac{1 \times 49}{3969} = \frac{49}{3969}$
* $\frac{1 \times 81}{3969} = \frac{81}{3969}$
* Add numerators: $49 + 81 = 130$.
* Result: $\frac{130}{3969}$.
3. $10^{-3} + (-9)^2$
* $10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001$.
* $(-9)^2 = -9 \times -9 = 81$.
* Add them: $81 + 0.001 = 81.001$.
4. $9^{-3} + (-9)^0$
* $9^{-3} = \frac{1}{9^3}$. Calculate $9^3$: $9 \times 9 = 81$, and $81 \times 9 = 729$. So, $\frac{1}{729}$.
* Any non-zero number to the power of 0 is 1. So, $(-9)^0 = 1$.
* Add them: $1 + \frac{1}{729} = 1 \frac{1}{729}$ (or $\frac{730}{729}$).
5. $4^{-2} + (-6)^3$
* $4^{-2} = \frac{1}{4^2} = \frac{1}{16}$.
* $(-6)^3 = -6 \times -6 \times -6$.
* $-6 \times -6 = 36$
* $36 \times -6 = -216$
* Add them: $\frac{1}{16} + (-216) = -216 + \frac{1}{16}$.
* As a mixed number: $-215 \frac{15}{16}$ (since you are adding a small positive fraction to a large negative integer, it moves slightly closer to zero).
* As an improper fraction: $-216 = -\frac{3456}{16}$. Then $-\frac{3456}{16} + \frac{1}{16} = -\frac{3455}{16}$.
6. $-9^2 + 3^3$
* Careful here: There are no parentheses around the 9 in $-9^2$. This means you square the 9 first, then apply the negative sign.
* $9^2 = 81$, so $-9^2 = -81$.
* $3^3 = 3 \times 3 \times 3 = 27$.
* Add them: $-81 + 27 = -54$.
7. $4^0 + 8^0$
* Any non-zero number to the power of 0 is 1.
* $4^0 = 1$.
* $8^0 = 1$.
* Add them: $1 + 1 = 2$.
8. $-3^0 + (-8)^2$
* $-3^0$: Again, no parentheses around the 3. $3^0 = 1$, so $-3^0 = -1$.
* $(-8)^2$: Parentheses mean the negative is included. $-8 \times -8 = 64$.
* Add them: $-1 + 64 = 63$.
9. $8^4 + 2^{-3}$
* $8^4 = 8 \times 8 \times 8 \times 8$.
* $8 \times 8 = 64$
* $64 \times 8 = 512$
* $512 \times 8 = 4096$
* $2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125$.
* Add them: $4096 + 0.125 = 4096.125$.
10. $(-2)^4 + (-0.02)^3$
* $(-2)^4 = -2 \times -2 \times -2 \times -2$.
* $(-2 \times -2) = 4$
* $(4 \times -2) = -8$
* $(-8 \times -2) = 16$
* $(-0.02)^3 = -0.02 \times -0.02 \times -0.02$.
* $0.02 \times 0.02 = 0.0004$
* $0.0004 \times -0.02 = -0.000008$
* Add them: $16 + (-0.000008) = 15.999992$.
Final Answer:
1. 162
2. 130/3969
3. 81.001
4. 730/729 (or 1 1/729)
5. -3455/16 (or -215 15/16)
6. -54
7. 2
8. 63
9. 4096.125
10. 15.999992
Parent Tip: Review the logic above to help your child master the concept of college math worksheets.
