$$\textbf{\textcolor{#4257b2}{Challenge}}$$

Write $9 \cdot 27 \cdot 3 \cdot 81$ as a power of $3$.

$$\textbf{\textcolor{#4257b2}{Challenge}}$$

Write each of the following as a power of $2$.

$$8^2$$

$$\textbf{\textcolor{#4257b2}{Mixed Review}}$$

There were $407$ books in the school library. The ninth grade returned $23$ books and checked out $17$; the tenth grade returned $15$ books and checked out $29$; the twelfth grade checked out $26$ books and returned $30$. How many books were left in the library?

Simplify.

$$\dfrac{x^9y^7}{x^2y^3}$$

Collect like terms and then arrange in descending order for the variable $m$.

$$-2m + 4m^3 - 7m + 9m^3 + 8$$

Tell whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial.

$$-43$$

Simplify. Express using exponents.

$$x^3 \cdot x^1$$

Multiply.

$$(4a - 7)(4a + 7)$$

Add.

$$(7x^3 + 6x^2 + 4x + 1) + (-7x^3 + 6x^2 - 4x + 5)$$

Multiply.

$$3y^2(6y^4 + 8y^3)$$

Simplify. Express using a positive exponent.

$$3^0$$

Subtract

$$(6x^5 - 3x^4 + x + 1) - (8x^5 + 3x^4 -1)$$

Multiply.

$$(7t^5)(4t^3)$$

Multiply.

$$(a - b)(a^3 + a^2b + ab^2 + b^3)$$