Question

Simplify the expression so there is only one power for each base

5.6^-5 x 3.4^-7 x 5.6^3 x 3.4^-4



Answers-

A) 5.6^-6 x3.4^-3

B) 5.6^-2 x 3.4 ^-11

C) 5.6^-8 x 3.4^-7

D) 5.6^-8 x 3.4^-3

E) 5.6^8 x 3.4^11

Answer 1

So, Correct option is B i.e
`5.6^(-2) * 3.4^(-11)\\`

Explanation:

The expression here contains exponents so, we will use exponent rule.

The exponent rule says that the power of the same bases can be added if two same bases are multiplied i.e.

`x^2 X y^2 X x^2 X y^1 \\can \,\, be \,\, written\,\, as\,\,\\x^(2+2) X y^(2+1)\\x^4 X y^3\\`

using this rule we can solve our question

`5.6^(-5) * 3.4^(-7) * 5.6^3 * 3.4^(-4)\\5.6^(-5+3) * 3.4^(-7-4)\\ 5.6^(-2) * 3.4^(-11)\\`

So, Correct option is B i.e
`5.6^(-2) * 3.4^(-11)`

Answer 2

`B)\: {5.6}^( - 2) * {3.4}^( - 11)`

step-by-step explanation

For the expression

`{5.6}^( - 5) * {3.4}^( - 7) * {5.6}^(3) * {3.4}^( - 4)`

we rewrite the expression to get

`{5.6}^( - 5) * {5.6}^(3) * {3.4}^( - 7) * {3.4}^( - 4)`

One of the laws of indices states that

`{a}^(m) * {a}^(n) = {a}^(m + n)`

which means that if multiplying expressions of the same bases, repeat one of the bases and add the exponents

This implies that

`{5.6}^( - 5) * {5.6}^(3) * {3.4}^( - 7) * {3.4}^( - 4)`

`={5.6}^(( - 5 + 3)) * {3.4}^( (-7 - 4))`

`={5.6}^(-2) * {3.4}^(-11)`