Exam 5: Exponents and Polynomials

The distance between the Sun and Mars is approximately $1.14 \times 10 ^ { 8 }$ miles. Use scientific notation to express this distance in feet. ( Hint: 5,280 feet = 1 mile.)

The distance between two planets is approximately $4.2 \times 10 ^ { 7 }$ miles. Use scientific notation to express this distance in feet. (5,280 feet = 1 mile.)

Find the product. $\left( - 2 a ^ { 2 } b \right) \left( - 2 a ^ { 3 } b ^ { 2 } \right) ( 5 a - 7 b )$

Write the following expression with a single exponent. Assume there is no division by 0. $\frac { b ^ { 9 m } } { b ^ { 7 m } }$

Find the product. $\left( 5 b ^ { 5 } \right) \left( 3 b ^ { 6 } \right)$

Write the number 55,000,000 in scientific notation.

Rewrite the polynomial with the powers in descending order. $14 b ^ { 2 } + 14 b ^ { 3 } + 9 b - 13$

Simplify the expression. $\left( 2 y ^ { 6 } c ^ { 9 } \right) ^ { 2 }$

Solve the equation. $( t + 2 ) ( t + 6 ) = t ^ { 2 } - 4$

Classify the following polynomial as a monomial, a binomial, or a trinomial. $- 9 b ^ { 2 } + 2 b - 5$

Solve the formula $V = J T$ for the variable $T$ .

Find the product. $( z + 5 ) ( z - 5 )$

Simplify the following expression. $x ^ { 6 } \cdot x ^ { 2 }$

Simplify the expression. $\left( 13 a ^ { 2 } + 6 a + 9 \right) + \left( 8 a ^ { 2 } + 9 a + 1 \right)$

Simplify the following expression. Do not use parentheses or negative exponents. $7 ^ { - 2 } \cdot 7 ^ { 3 } \cdot 7 ^ { - 4 }$

Simplify. $\left( 15 ^ { 5 } \right) ^ { 3 }$

Find the product. $6 ( 3 t + 5 ) ( t - 4 )$

Find the sum when $8 x ^ { 2 } + 3 x - 3$ is added to the sum of $- 2 x ^ { 2 } - 7 x + 4$ and $- 9 x ^ { 2 } + 8 x - 4$ .

Write the polynomial with the exponents on $x$ in descending order. $4 x - 3 x ^ { 4 } + 13 - 6 x ^ { 2 }$

In the expression $- 2 ^ { 15 }$ , what is the base and the exponent?