Question

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Answer 1

Answer:

1. -1

2. 1/27

3.343/1000 OR 0.343

HOPE IT HELPS!

Answer 2

Answer:

1. 1

2. $\frac{1}{27}$

3. $\frac{343}{1000}$

4. 5

Step-by-step explanation:

1. According to the a rule of exponents, any number x to the power 0 i.e.

$x^{0}$= 1

2. Since the power for $3^{-3}$ is negative, the base i.e. 3 will be shifted to the denominator i.e. making it $\frac{1}{3^{3} }$ = $\frac{1}{27}$.

3. The same rule from 2nd question applies to this one. Firstly we solve the rational number in the brackets.

When you apply the power to both numerator and denominator $(\frac{7}{3} )^{3}$ becomes $\frac{343}{8}$.

Now when you change $5^{-3}$ using the previous rule of shifting the base to denominator (since power is negative), you get $\frac{1}{5}$.

Now when you operate on $\frac{343}{8}$×$\frac{1}{5}$, you get the answer $\frac{343}{1000}$

4. For this one we can use the rule from previous question and the rule for multiplication of powers, which says if you have an expression in the form of $(a^{n})^{m}$, then it becomes $a^{mn}$ as both the powers get multiplied.

So, if you multiply both the powers in the expression $(5^{-1})^{-1}$, you get 5 as -1 × -1 = 1 and $5^{1} = 5$

I hope my explanation was helpful for you.