Here are the calculations for the next set of problems: i) Calculate 3⁴ Step 1: Expand the exponent. 3⁴ = 3 × 3 × 3 × 3 Step 2: Multiply the numbers. 3 × 3 × 3 × 3 = 81 The value is 81. j) Calculate 5² Step 1: Expand the exponent. 5² = 5 × 5 Step 2: Multiply the numbers. 5 × 5 = 25 The value is 25. k) Calculate 3⁴ × 3² Step 1: Apply the exponent rule a^m × aⁿ = a^(m+n). 3⁴ × 3² = 3⁴⁺² Step 2: Add the exponents. 3⁴⁺² = 3⁶ Step 3: Expand and multiply. 3⁶ = 3 × 3 × 3 × 3 × 3 × 3 = 729 The value is 729. l) Calculate 5⁵ ÷ 5³ Step 1: Apply the exponent rule a^m ÷ aⁿ = a^(m−n). 5⁵ ÷ 5³ = 5⁵⁻³ Step 2: Subtract the exponents. 5⁵⁻³ = 5² Step 3: Expand and multiply. 5² = 5 × 5 = 25 The value is 25.

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Expand the exponent.

April 18, 2026Mathematics

ScanSolve AI Answer

Answer

\text{81}

\text{25}

\text{729}

Step-by-step solution

10 steps

Here are the calculations for the next set of problems:

i) Calculate $3^4$

Expand the exponent.
$3^4 = 3 \times 3 \times 3 \times 3$
Multiply the numbers.
$3 \times 3 \times 3 \times 3 = 81$
The value is $\boxed{\text{81}}$ .

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

k) Calculate $3^4 \times 3^2$
Apply the exponent rule $a^m \times a^n = a^{m+n}$ .
$3^4 \times 3^2 = 3^{4+2}$
Add the exponents.
$3^{4+2} = 3^6$
Expand and multiply.
$3^6 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729$
The value is $\boxed{\text{729}}$ .

l) Calculate $5^5 \div 5^3$
Apply the exponent rule $a^m \div a^n = a^{m-n}$ .
$5^5 \div 5^3 = 5^{5-3}$
Subtract the exponents.
$5^{5-3} = 5^2$
Expand and multiply.
$5^2 = 5 \times 5 = 25$
The value is $\boxed{\text{25}}$ .

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Expand the exponent.

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Step-by-step solution