Expand the exponent.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the calculations for the next set of problems:
i) Calculate $3^4$
Step 1: Expand the exponent.
$$3^4 = 3 \times 3 \times 3 \times 3$$
Step 2: Multiply the numbers.
$$3 \times 3 \times 3 \times 3 = 81$$
The value is $\boxed{\text{81}}$.
j) Calculate $5^2$
Step 1: Expand the exponent.
$$5^2 = 5 \times 5$$
Step 2: Multiply the numbers.
$$5 \times 5 = 25$$
The value is $\boxed{\text{25}}$.
k) Calculate $3^4 \times 3^2$
Step 1: Apply the exponent rule $a^m \times a^n = a^{m+n}$.
$$3^4 \times 3^2 = 3^{4+2}$$
Step 2: Add the exponents.
$$3^{4+2} = 3^6$$
Step 3: 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 $5^5 \div 5^3$
Step 1: Apply the exponent rule $a^m \div a^n = a^{m-n}$.
$$5^5 \div 5^3 = 5^{5-3}$$
Step 2: Subtract the exponents.
$$5^{5-3} = 5^2$$
Step 3: Expand and multiply.
$$5^2 = 5 \times 5 = 25$$
The value is $\boxed{\text{25}}$.
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