Answer to Question #95895 in Algebra for MelkinJosue

Question

Which expression is equivalent to the one below?

(2^6 x 9^6) divided 18^{14}

Answer 1

Solution:

We need to find the Equivalent Expression to ( 2⁶ x 9⁶ ) Divided by 18¹⁴

Step1:

In the Multiplication of two terms with same exponent, we can multiply the bases and write the same exponent for the result

of multiplication.

For example,

a^m x b ^m = ( a x b )^m

so, 2⁶ x 9⁶ = ( 2 x 9 )⁶ = 18⁶

Step 2:

In the division of two terms with same base and different exponents, we can write the base at the numerator and the exponent can be written as 'numerator exponent - denominator's exponent'.

For example.

a^m / aⁿ = a ^{( m - n)}

( 2⁶ x 9⁶ ) Divided by  18¹⁴ = (18)⁶ / 18¹⁴ = 18^{6 - 14} = 18 ^{- 8} = 1/ (18⁸)

Answer: 18 ^{- 8} = 1/ 18⁸.