Question

Use the properties of exponents to write an equivalent expression that is a product of distinct primes, each raised to an integer power for the expression (${10}^6$$\times$ $9^2$)/$6^4$

• A. $2^3$\times5^6$
• B. $2^3$\times5^5$
• C. $2^2$\times5^6$
• D. $2^2$\times5^5$

Answer 1

The correct option is C $2^2$\times5^6$

Given expression: (${10}^6\times 9^2$)/$6^4$
= $(2\times 5{)}^6\times (3^2{)}^2/(2\times 3{)}^4$
= $2^6\times 5^6\times 3^4$ / $2^4\times 3^4$
= $2^{6-4}\times 5^6\times 3^{4-4}$
= $2^2\times 5^6$