Step: 1

(- 3)^{-4}

[Original expression.]

Step: 2

= 1 ( - 3 ) 4

[A base with negative exponent is expressed as a ^{- n} = 1 a n .]

Step: 3

= 1 ( - 3 ) 4 = 1 81

Step: 4

The expression (-3)^{-4} is equal to 1 81 in fraction form.

Correct Answer is : 1 81

Step: 1

- (5)^{- 3} = - 1 5 3

[A base with negative exponent is expressed as a ^{- n} = 1 a n .]

Step: 2

(5)^{3} = 125

Step: 3

- 1 5 3 = - 1 1 2 5

Step: 4

The expression - (5)^{- 3} in the form of fraction is - 1 1 2 5 .

Correct Answer is : - 1 1 2 5

Step: 1

(- d )^{-6}

[Original expression.]

Step: 2

= 1 ( - d ) 6

[By definition of a negative exponent a ^{- n} = 1 a n ]

Step: 3

= 1 d 6

Step: 4

The expression (- d )^{-6} using a positive exponent is 1 d 6 .

Correct Answer is : 1 d 6

Step: 1

7^{3} × 7^{a} = 7^{7}

[Original equation.]

Step: 2

= 7^{3 + a} = 7^{7}

[Use product of powers property.]

Step: 3

3 + a = 7

[Since the bases are same, the powers should be equal.]

Step: 4

[Simplify.]

Step: 5

The value of a is 4 .

Correct Answer is : 4

Step: 1

5^{3} × 5^{4} = 5^{(3 + 4)}

[Use product of powers property.]

Step: 2

= 5^{7}

[Add the exponents.]

Step: 3

5^{3} × 5^{4}, expressed as single power of the base is 5^{7}.

Correct Answer is : 5^{7}

Step: 1

[Original expression.]

Step: 2

= (-5)^{3 - 7}

[Use quotient of powers property.]

Step: 3

= (-5)^{-4}

[Subtract exponents.]

Step: 4

= 1 ( - 5 ) 4

[Use definition of negative exponent.]

Step: 5

= 1 6 2 5

[Evaluate power.]

Correct Answer is : 1 625

Step: 1

7^{ - 5} × 7^{10} = 7^{ - 5 + 10}

[Use the product of powers property.]

Step: 2

= 7^{5}

[Add exponents.]

Step: 3

= 16807

[Evaluate the power.]

Step: 4

The value of the expression is 16807.

Correct Answer is : 16807

Step: 1

(- 3)^{- 4} × (- 3)^{2} = (- 3)^{- 4 + 2}

[Use the product of powers property.]

Step: 2

= (- 3)^{- 2}

[Add exponents.]

Step: 3

= 1 ( - 3 ) 2

[Use the negative exponent definition.]

Step: 4

= 1 9

[Evaluate the power.]

Step: 5

The value of the expression is 1 9 .

Correct Answer is : 1 9

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- Exponent