Which expression is equivalent to 6^6 * 10^6? Choices: (A)1/60^6 (B)60^12 (C)60^36 (D)60^6

Understand the problem: Understand the problem. We need to find an expression equivalent to the multiplication of 6^6 and 10^6.Use property of exponents: Use the property of exponents for multiplication. When multiplying two powers that have the same exponent but different bases, we can multiply the bases and keep the exponent the same. 6^6 * 10^6 = (6*10)^6Calculate new base: Calculate the new base. Multiply the bases 6 and 10. 6 * 10 = 60Apply new base to exponent: Apply the new base to the exponent. Replace the multiplied bases with the single base of 60. (6*10)^6 = 60^6Match with given choices: Match the result with the given choices. The equivalent expression is 60^6, which matches choice (D).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expression is equivalent to $6^6 \times 10^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{60^6}$ $\newline$ (B) $60^{12}$ $\newline$ (C) $60^{36}$ $\newline$ (D) $60^6$

View step-by-step help

Home

Math Problems

Grade 8

Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

6^6 \times 10^6

\newline

Choices:

\newline

(A)

\frac{1}{60^6}

\newline

(B)

60^{12}

\newline

(C)

60^{36}

\newline

(D)

60^6

Understand the problem: Understand the problem. $\newline$ We need to find an expression equivalent to the multiplication of $6^6$ and $10^6$ .
Use property of exponents: Use the property of exponents for multiplication. $\newline$ When multiplying two powers that have the same exponent but different bases, we can multiply the bases and keep the exponent the same. $\newline$ $6^6 \times 10^6 = (6\times10)^6$
Calculate new base: Calculate the new base. $\newline$ Multiply the bases $6$ and $10$ . $\newline$ $6 \times 10 = 60$
Apply new base to exponent: Apply the new base to the exponent. $\newline$ Replace the multiplied bases with the single base of $60$ . $\newline$ $(6\times10)^6 = 60^6$
Match with given choices: Match the result with the given choices. $\newline$ The equivalent expression is $60^6$ , which matches choice (D).