Multiplication of Powers: Solving the problem

Solve the exercise:

$Y^2+Y^6-Y^5\cdot Y=$

We use the power property to multiply terms with identical bases:

$a^m\cdot a^n=a^{m+n}$We apply it in the problem:

$Y^2+Y^6-Y^5\cdot Y=Y^2+Y^6-Y^{5+1}=Y^2+Y^6-Y^6=Y^2$When we apply the previous property to the third expression from the left in the sum, and then simplify the total expression by adding like terms.

Therefore, the correct answer is option D.

$Y^2$

$\frac{9\cdot3}{8^0}=\text{?}$

We use the formula:

$a^0=1$

$\frac{9\times3}{8^0}=\frac{9\times3}{1}=9\times3$

We know that:

$9=3^2$

Therefore, we obtain:

$3^2\times3=3^2\times3^1$

We use the formula:

$a^m\times a^n=a^{m+n}$

$3^2\times3^1=3^{2+1}=3^3$

$3^3$

$\frac{9^2\cdot3^{-4}}{6^3}=\text{?}$

$6^{-3}$

$3^{-3}\cdot\frac{19^{35}\cdot19^{-32}}{19^3}=\text{?}$

$\frac{1}{27}$

$9^4\cdot3^{-8}\cdot\frac{1}{3}=\text{?}$

$3^{-1}$

Solve the following:

$\frac{35x\cdot y^7}{7xy}\cdot\frac{8x}{5y}=$

$8xy^5$

Calculate and indicate the answer:

$(\sqrt{8}\cdot\sqrt{2}-\sqrt{9})^2:2^2+3^2$

$\frac{1}{13}$