How can -2 be used as a base to write 32?

(- 2)^{5} \times (- 1)^{5}

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(- 2)^{5} \times 1^{5}

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(- 2)^{5} \times (- 1)^{0}

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(- 2)^{5} \times 1^{0}

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Solution

The correct option is A $(- 2)^{5} \times (- 1)^{5}$
32, a positive number, can be generated from a negative base only if it is multiplied by another negative number.
$(- 2)^{5} \times (- 1)^{5}$ = $(- 2)^{5} \times (- 1)$ = $(- 32) \times (- 1)$ = $32$

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Similar questions

Q. How many 3 digit numbers in base 10 are there which can be expressed using 3 digits in base 9 as well as in base 11?

Question 153(ii)

In a repeater machine with 0 as an exponent, the base machine is applied 0 times.
What do you think the value of $6^{o}$ is ?
You have seen that a hook up of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression.
Asif Raza thought about how he could rewrite the expression $2^{2} 0 \times 2^{5}$ .

Asif Raza's idea is one of the product laws of exponents, which can be expressed like this
Multiplying Expressions with the same base $a^{b} \times a^{c} = a^{b + c}$
Actually, this law can be used with more than two expressions. As long as the bases are the same, to find the product you can add the exponents and use the same base.
e.g. $3^{2} \times 3^{3} \times 3^{10} = 3^{2 + 3 + 10} = 3^{15}$

Question 153(ii)

Q. Raw materials used in various industries can be classified as marine based, forest based, agro based and ________.

Q. can be used to test the presence of a base.

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How can -2 be used as a base to write 32?

The correct option is A (−2)5×(−1)532, a positive number, can be generated from a negative base only if it is multiplied by another negative number. (−2)5×(−1)5 = (−2)5×(−1) = (−32)×(−1) = 32

The correct option is A $(- 2)^{5} \times (- 1)^{5}$
32, a positive number, can be generated from a negative base only if it is multiplied by another negative number.
$(- 2)^{5} \times (- 1)^{5}$ = $(- 2)^{5} \times (- 1)$ = $(- 32) \times (- 1)$ = $32$