Powers Exponents Roots and Radicals (Upload)

Simplify.

\(\frac{ \left( -5 \right) ^{2} \left( -5 \right) ^{-2}}{ \left( -5 \right) ^{-3}}\)

Simplify.

\(\frac{ \left( -7 \right) ^{2}}{ \left( -7 \right) ^{-1}}\)

Simplify.

\(\left( \left( 2^{-2} \right) ^{-1} \right) ^{-2}\)

Simplify.

\(\left( 6^{3} \right) ^{-1}\)

Simplify.

\(\left( \frac{x^{-2}}{y^{2}} \right) ^{3}\)

Simplify.

\(\frac{x^{2}y^{-2}}{x^{-3}y^{3}}\)

One online seller has about 6 x 10⁸ online orders, and another online seller has about 5 x 10⁷ online orders. How many times more orders does the first company have?

Solve.

\(x^{2}=121\)

Simplify.

\(3^{3} \times 3^{-4} \times 3^{0}\)

Simplify.

\(\left( 9x^{-2}y^{3} \right) ^{2}\)

Simplify.

\(\left( \frac{x^{5}}{5} \right) ^{4}\)

The land area of Colorado about 1 x 10⁵ square miles, and the land area of Ohio is about 4 x 10⁴ square miles. How many times larger is the land area of Colorado?

The population of China is about 1 x 10⁹,and the population of the United States is about 3 x 10⁸. How many times larger is the population of China than the population of the United States? 

The error in connecting two pipes for one house is 3 x 10⁻⁵meter, and the error in connecting two pipes for a second house is about 1 x 10⁻⁶ meter. How many times larger is the error in the first house?

Solve.

\(x^{3}=125\)

Solve.

\(x^{3}=343\)

Solve.

x² = 225

Simplify.

\(\left( \frac{xy^{0}}{z^{2}} \right) ^{2}\)

Simplify.

\( \left( \frac{x^{3}y^{-2}}{x^{-2}y^{3}} \right) ^{5}\)

Simplify.

\(\left( x^{2}y^{3}z^{-1} \right) ^{3}\)

Simplify.

\(5^{6} \times 5^{-3}\)

The error on one manufacturing machine is 2 x 10⁻⁴ and the error on a second machine is 8 x 10⁻⁵ How many times larger is the error on the first machine?

A lysosome has a length of 1 x 10⁻⁶ meter, and measles virus has a length of  2 x 10⁻⁹ meter. How many times longer is the lysosome?

One cell has a diameter of 5 x 10⁻⁸ meter, and another cell has a diameter of  6 x 10⁻⁹ meter. How many times larger is the first cell?

Simplify.

\(\left( 4x^{3} \right) ^{2}\)

Simplify.

\(\left( 2x^{2} \right) ^{4}\)

One athlete had a salary of about 3 x 10⁷ dollars per year and another athlete had a salary of about 2 x 10⁶ dollars per year. How many times larger is the salary of the first athlete?

A red blood cell has a length of  8 x 10⁻⁶ meter, and a skin cell has a length of 3 x 10⁻⁵ meter. How many times larger is the skin cell?

The landmass of the United States is about 4 x 10⁶ square miles, and the landmass of Alaska is about 7 x 10⁵ square miles. How many times larger is the landmass of the United States than the landmass of Alaska?

Simplify.

\(\left( 3^{2} \right) ^{3}\)

Simplify.

\(\left( \frac{x^{0}}{y^{-2}} \right) ^{2}\)