Question

How do you rewrite ${7^4}{.7^5}$ using a single exponent ?

Answer 1

Hint:To rewrite the given expression with a single exponent use the law of indices for multiplication. And simply rewrite the given expression with a single exponent.Law of indices for multiplication is given as follows: ${x^m} \times {x^n} = {x^{m + n}}$.

Complete step by step answer:
In order to rewrite the given expression ${7^4}{.7^5}$ using a single exponent, since in the given expression the base of all multiplicands are same, so we will use law of indices for multiplication in order to simplify it as a exponent as follows. Now, we will use law of indices for multiplication in order to multiply the similar base exponents, present in the expression.

Law of indices for multiplication is given as when “x” to the power of “m” is being multiplied with “x” to the power of “n”, then their product is given as “x” to the power of sum of “m” and “n”. In simple words, if bases of multiplicands are equal then their product is given as base to the power of sum of the exponents of the multiplicands. Mathematically it can be understood as follows
${x^m} \times {x^n} = {x^{m + n}}$
Using this to our expression, we will get
$\therefore {7^4}{.7^5} = {7^{4 + 5}} = {7^9}$

Therefore ${7^9}$ is the simplified version of ${7^4}{.7^5}$ in single exponent.

Note:Law of indices is very useful in simplifying problems consisting of exponents. Apart from law of indices for multiplication, there are several ones like law of indices for division, for fractional powers, for zero power, for negative powers and law of indices for brackets.