Here are the step-by-step solutions for each exponential expression.
1) $\frac{14a^{10}}{7a^8}$
* Divide the numbers: $14 \div 7 = 2$
* Subtract the exponents for $a$: $10 - 8 = 2$
* Result:
$2a^2$
2) $(-19r^6)(-5r^5)$
* Multiply the numbers: $-19 \times -5 = 95$ (negative times negative is positive)
* Add the exponents for $r$: $6 + 5 = 11$
* Result:
$95r^{11}$
3) $(-3m^{-3})(9m^{14})$
* Multiply the numbers: $-3 \times 9 = -27$
* Add the exponents for $m$: $-3 + 14 = 11$
* Result:
$-27m^{11}$
4) $\frac{2s^9}{18s^{-6}}$
* Simplify the fraction: $2 \div 18 = \frac{1}{9}$
* Subtract the bottom exponent from the top: $9 - (-6) = 9 + 6 = 15$
* Result:
$\frac{s^{15}}{9}$ or
$\frac{1}{9}s^{15}$
5) $\frac{6n^8}{8n^7}$
* Simplify the fraction: $6 \div 8 = \frac{3}{4}$
* Subtract the exponents for $n$: $8 - 7 = 1$
* Result:
$\frac{3n}{4}$ or
$\frac{3}{4}n$
6) $(6z^{10})(11z^{-2})$
* Multiply the numbers: $6 \times 11 = 66$
* Add the exponents for $z$: $10 + (-2) = 8$
* Result:
$66z^8$
7) $(15v^{-9})(-2v^{-2})$
* Multiply the numbers: $15 \times -2 = -30$
* Add the exponents for $v$: $-9 + (-2) = -11$
* Result:
$-30v^{-11}$ or
$-\frac{30}{v^{11}}$
8) $\frac{20u^{-4}}{5u^{12}}$
* Divide the numbers: $20 \div 5 = 4$
* Subtract the bottom exponent from the top: $-4 - 12 = -16$
* Result:
$4u^{-16}$ or
$\frac{4}{u^{16}}$
Final Answer:
1) $2a^2$
2) $95r^{11}$
3) $-27m^{11}$
4) $\frac{s^{15}}{9}$
5) $\frac{3n}{4}$
6) $66z^8$
7) $-30v^{-11}$
8) $4u^{-16}$
Parent Tip: Review the logic above to help your child master the concept of simplify expressions with exponents worksheet.
