Question

(-9/8)^5 × 4^7 simplify​

Answer 1

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x4" was replaced by "x^4".

STEP

1

:

1.1 4 = 22

(4)7 = (22)7 = 214

Equation at the end of step

1

:

-9

{——}5 • x) • (x2^14)

8

STEP

2

:

-9

Simplify ——

8

Equation at the end of step

2

:

-9

((——)5) • x) • x16384

8

STEP

3

:

3.1

Negative number raised to an odd power is negative

To show this we begin with (-7)5 ,a negative number raised to an odd exponent:

(-7)5 can be written as (-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)5 can be written as (49)•(49)•(-7) which is a negative number.

We showed that (-7)5 is a negative number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 5 by any odd exponent, we proved which had to be proved

3.2 9 = 32 (-9)5 = (32)5 = 310 3.3 8 = 23 (8)5 = (23)5 = 215

Equation at the end of step

3

:

-310

(———— • x) • x16384

215

STEP

4

:

Multiplying exponential expressions

4.1 x1 multiplied by x16384 = x(1 + 16384) = x16385

Final result :

-310x16385

——————————

215