Question

which expression is equivalent to ( 9^5 )?
( 9 \times 5 )
( 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 )
( 9 \times 9 \times 9 \times 9 \times 9 )
( 9 \times 9 \times 9 \times 9 \times 9 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 )

Explanation:

Step1: Recall exponent definition

An exponent \(a^n\) means multiplying \(a\) by itself \(n\) times, i.e., \(a^n=\underbrace{a\times a\times\cdots\times a}_{n\text{ times}}\).

Step2: Analyze each option

• Option 1: \(9\times5\) is a product of 9 and 5, not related to exponentiation of a single base.
• Option 2: \(5\times5\times\cdots\times5\) (9 times) is \(5^9\), not \(g^5\) (unless \(g = 5\) and exponent is 9, which doesn't match).
• Option 3: If we assume \(g = 9\), then \(g^5=9^5 = 9\times9\times9\times9\times9\), which matches the exponent definition.
• Option 4: This is a product of \(9^6\) and \(5^8\), not equivalent to \(g^5\).

Answer:

C. \(9\times9\times9\times9\times9\) (assuming there is a typo and \(g = 9\), or if \(g\) is a base, the exponent \(5\) means multiplying the base by itself 5 times, so \(g^5 = g\times g\times g\times g\times g\), and if \(g = 9\), then it's \(9\times9\times9\times9\times9\))