Question

$\frac{5^4 × 5^3}{5^7}=?$

• A. 1
• B. 58
• C. 25
• D. 5

Answer 1

Answer:

A. 1

The value of the expression is 1.

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This problem can be easily solved using the laws of exponents.

Step 1: Simplify the numerator

When multiplying numbers with the same base, you add their exponents ($a^m \times a^n = a^{m+n}$):
$5^4 \times 5^3 = 5^{4 + 3} = 5^7$

The equation now looks like this:
$\frac{5^7}{5^7}$

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Step 2: Divide the values

Any non-zero number divided by itself is equal to 1 ($\frac{a^m}{a^m} = 1$):
$\frac{5^7}{5^7} = \mathbf{1}$

(Alternatively, using subtraction rule for division $a^m \div a^n = a^{m-n}$: $5^{7 - 7} = 5^0 = 1$)