Exponents with Multiplication & Division - SmartMathz - Free Printable

To solve the given problems involving exponents, multiplication, and division, we will carefully evaluate each expression step by step. Let's go through each problem:

---

Problem 1:

\[
\frac{(-5)^1}{1^{21}}
\]

- Step 1: Simplify the numerator \((-5)^1\):
\[
(-5)^1 = -5
\]

- Step 2: Simplify the denominator \(1^{21}\):
\[
1^{21} = 1
\]

- Step 3: Divide the numerator by the denominator:
\[
\frac{-5}{1} = -5
\]

Answer:
\[
\boxed{-5}
\]

---

Problem 2:

\[
\frac{8^2}{(-9)^0}
\]

- Step 1: Simplify the numerator \(8^2\):
\[
8^2 = 64
\]

- Step 2: Simplify the denominator \((-9)^0\):
\[
(-9)^0 = 1 \quad \text{(Any non-zero number raised to the power of 0 is 1)}
\]

- Step 3: Divide the numerator by the denominator:
\[
\frac{64}{1} = 64
\]

Answer:
\[
\boxed{64}
\]

---

Problem 3:

\[
\frac{(-1)^3}{6^1}
\]

- Step 1: Simplify the numerator \((-1)^3\):
\[
(-1)^3 = -1
\]

- Step 2: Simplify the denominator \(6^1\):
\[
6^1 = 6
\]

- Step 3: Divide the numerator by the denominator:
\[
\frac{-1}{6} = -\frac{1}{6}
\]

Answer:
\[
\boxed{-\frac{1}{6}}
\]

---

Problem 4:

\[
\frac{15^3}{(-5)^3}
\]

- Step 1: Simplify the numerator \(15^3\):
\[
15^3 = 15 \times 15 \times 15 = 3375
\]

- Step 2: Simplify the denominator \((-5)^3\):
\[
(-5)^3 = -5 \times -5 \times -5 = -125
\]

- Step 3: Divide the numerator by the denominator:
\[
\frac{3375}{-125} = -27
\]

Answer:
\[
\boxed{-27}
\]

---

Problem 5:

\[
\frac{(-4)^3}{2^2}
\]

- Step 1: Simplify the numerator \((-4)^3\):
\[
(-4)^3 = -4 \times -4 \times -4 = -64
\]

- Step 2: Simplify the denominator \(2^2\):
\[
2^2 = 4
\]

- Step 3: Divide the numerator by the denominator:
\[
\frac{-64}{4} = -16
\]

Answer:
\[
\boxed{-16}
\]

---

Problem 6:

\[
2^4 \times (-3)^4
\]

- Step 1: Simplify \(2^4\):
\[
2^4 = 2 \times 2 \times 2 \times 2 = 16
\]

- Step 2: Simplify \((-3)^4\):
\[
(-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81
\]

- Step 3: Multiply the results:
\[
16 \times 81 = 1296
\]

Answer:
\[
\boxed{1296}
\]

---

Problem 7:

\[
1^9 \times (-10)^2
\]

- Step 1: Simplify \(1^9\):
\[
1^9 = 1
\]

- Step 2: Simplify \((-10)^2\):
\[
(-10)^2 = (-10) \times (-10) = 100
\]

- Step 3: Multiply the results:
\[
1 \times 100 = 100
\]

Answer:
\[
\boxed{100}
\]

---

Problem 8:

\[
(-10)^3 \times (-6)^2
\]

- Step 1: Simplify \((-10)^3\):
\[
(-10)^3 = (-10) \times (-10) \times (-10) = -1000
\]

- Step 2: Simplify \((-6)^2\):
\[
(-6)^2 = (-6) \times (-6) = 36
\]

- Step 3: Multiply the results:
\[
-1000 \times 36 = -36000
\]

Answer:
\[
\boxed{-36000}
\]

---

Problem 9:

\[
1^{19} \times (-7)^1
\]

- Step 1: Simplify \(1^{19}\):
\[
1^{19} = 1
\]

- Step 2: Simplify \((-7)^1\):
\[
(-7)^1 = -7
\]

- Step 3: Multiply the results:
\[
1 \times -7 = -7
\]

Answer:
\[
\boxed{-7}
\]

---

Problem 10:

\[
4^3 \times (-2)^2
\]

- Step 1: Simplify \(4^3\):
\[
4^3 = 4 \times 4 \times 4 = 64
\]

- Step 2: Simplify \((-2)^2\):
\[
(-2)^2 = (-2) \times (-2) = 4
\]

- Step 3: Multiply the results:
\[
64 \times 4 = 256
\]

Answer:
\[
\boxed{256}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -5 \\
2. & 64 \\
3. & -\frac{1}{6} \\
4. & -27 \\
5. & -16 \\
6. & 1296 \\
7. & 100 \\
8. & -36000 \\
9. & -7 \\
10. & 256 \\
\end{array}
}
\]