Which applies the power of a power rule properly to simplify the expression (710)5?

2 answers:

6 0

The power to a power rule is : KEEP THE BASE AND MULTIPLY THE POWERS.
Ex. (x^3)^4 = x^(3*4) = x^12

So ....
(7^10)^5 = 7^50
Last option is correct.

Ne4ueva [31]2 years ago

3 0

Answer:

(7^10)^5= 7^50

Step-by-step explanation:

Givene expression is

(7^10)^5

we apply power of power rule

(a^m)^n = (a)^mn

As per this property we multiply the outside exponent with the exponent inside. multiply the exponent 10 and 5 that gives us 50

$(7^{10}) ^ 5= 7^{10*5} = 7^{50}$

So (7^10)^5= 7^50

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Explain how negative powers of 10 can be helpful when writing and comparing small numbers

Luba_88 [7]

Answer:

See explanation

Step-by-step explanation:

Powers of 10 is a very useful way of writing down large or small numbers.

Instead of having lots of zeros, you show how many powers of 10 will make that many zeros.

When you work with small numbers, you should use the negative powers of 10. Just remember for negative powers of 10, move the decimal point to the left. For example,

$0.36=3.6\cdot 10^{-1}\ [\text{Move the decimal point one place to the left}]\\ \\0.036=3.6\times 10^{-2}\ [\text{Move the decimal point two places to the left}]\\ \\0.0036=3.6\times 10^{-3}\ [\text{Move the decimal point three places to the left}]\\ \\...$

When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then

if the powers of 10 are the same in compared numbers are the same, just compare the numbers which are multiplied by these powers of 10. For example, $3.6\times 10^{-6}>2.6\times 10{-6},$ because powers are the same (-6) and $3.6>2.6$
if the powers are different, then the smaller is power, the smaller is number (number with the smaller negative power has more places after decimal point). For example, $3.6\times 10^{-6}> 2.6\times 10^{-7},$ because $-6>-7$