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Which expression is equivalent to $6^4 \times 10^4$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{60^4}$ $\newline$ (B) $60^8$ $\newline$ (C) $60^{16}$ $\newline$ (D) $60^4$

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Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

6^4 \times 10^4

?

\newline

Choices:

\newline

(A)

\frac{1}{60^4}

\newline

(B)

60^8

\newline

(C)

60^{16}

\newline

(D)

60^4

Understand the expression: Understand the given expression. $\newline$ We need to find an expression equivalent to $6^4 \times 10^4$ . This involves two numbers, $6$ and $10$ , both raised to the power of $4$ and then multiplied together.
Use exponent property for multiplication: Use the property of exponents for multiplication. $\newline$ When multiplying two powers with the same exponent but different bases, we can multiply the bases first and then apply the exponent to the result. $\newline$ $6^4 \times 10^4 = (6 \times 10)^4$
Calculate product of bases: Calculate the product of the bases. $\newline$ Multiply the bases $6$ and $10$ before applying the exponent. $\newline$ $6 \times 10 = 60$
Apply exponent to product: Apply the exponent to the product of the bases. $\newline$ Now that we have the product of the bases, we raise it to the power of $4$ . $\newline$ $(6 \times 10)^4 = 60^4$
Match with given choices: Match the result with the given choices. $\newline$ The expression $60^4$ matches with choice (D) $60^4$ .

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