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Calculate powers and products/quotients of powers.

April 18, 2026Mathematics

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Answers

4 parts

\text{8}

\text{25}

\text{32}

\text{25}

Step-by-step solution

10 steps

Here are the calculations for question 4:

Part a· 2 steps

Calculate $2^3$

Expand the exponent.
$2^3 = 2 \times 2 \times 2$
Multiply the numbers.
$2 \times 2 \times 2 = 8$
The value is $\boxed{\text{8}}$ .

Part b· 2 steps
$\text{25}$

Calculate $5^2$

Expand the exponent.
$5^2 = 5 \times 5$
Multiply the numbers.
$5 \times 5 = 25$
The value is $\boxed{\text{25}}$ .

Part c· 3 steps
$\text{32}$

Calculate $2^3 \times 2^2$

Apply the exponent rule $a^m \times a^n = a^{m+n}$ .
$2^3 \times 2^2 = 2^{3+2}$
Add the exponents.
$2^{3+2} = 2^5$
Expand and multiply.
$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$
The value is $\boxed{\text{32}}$ .

Part d· 3 steps
$\text{25}$

Calculate $5^4 \div 5^2$

Apply the exponent rule $a^m \div a^n = a^{m-n}$ .
$5^4 \div 5^2 = 5^{4-2}$
Subtract the exponents.
$5^{4-2} = 5^2$
Expand and multiply.
$5^2 = 5 \times 5 = 25$
The value is $\boxed{\text{25}}$ .

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Calculate powers and products/quotients of powers.

Answers

Step-by-step solution

Part a· 2 steps

Expand the exponent.

Multiply the numbers.

Part b· 2 steps25\text{25}25

Expand the exponent.

Multiply the numbers.

Part c· 3 steps32\text{32}32

Apply the exponent rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Add the exponents.

Expand and multiply.

Part d· 3 steps25\text{25}25

Apply the exponent rule am÷an=am−na^m \div a^n = a^{m-n}am÷an=am−n.

Subtract the exponents.

Expand and multiply.

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More Mathematics Questions

Part b· 2 steps
$\text{25}$

Part c· 3 steps
$\text{32}$

Apply the exponent rule $a^m \times a^n = a^{m+n}$ .

Part d· 3 steps
$\text{25}$

Apply the exponent rule $a^m \div a^n = a^{m-n}$ .