Which expression is equivalent to 6^4 * 10^4? Choices: (A)1/60^4 (B)60^8 (C)60^16 (D)60^4

Understand the expression: Understand the given expression. We need to find an expression equivalent to 6^4 * 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. 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. 6^4 * 10^4 = (6 * 10)^4Calculate product of bases: Calculate the product of the bases. Multiply the bases 6 and 10 before applying the exponent. 6 * 10 = 60Apply exponent to product: Apply the exponent to the product of the bases. Now that we have the product of the bases, we raise it to the power of 4. (6 * 10)^4 = 60^4Match with given choices: Match the result with the given choices. The expression 60^4 matches with choice (D) 60^4.

Home

Math Problems

Grade 8

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) $60^4$ .