Simplify (15a^0b^2c^34)(3a^16b^-29c^0)

$(15 a^{0} b^{2} c^{34}) (3 a^{16} b^{- 29} c^{0})$

Step 1

Multiply $a^{0}$ by $a^{16}$ by adding the exponents.

Move $a^{16}$ .

$15 (a^{16} a^{0}) b^{2} c^{34} (3 b^{- 29} c^{0})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 a^{16 + 0} b^{2} c^{34} (3 b^{- 29} c^{0})$

Add $16$ and $0$ .

$15 a^{16} b^{2} c^{34} (3 b^{- 29} c^{0})$

Step 2

Simplify $15 a^{16} b^{2} c^{34} (3 b^{- 29} c^{0})$ .

$15 a^{16} b^{2} c^{34} (3 b^{- 29})$

Step 3

Multiply $b^{2}$ by $b^{- 29}$ by adding the exponents.

Move $b^{- 29}$ .

$15 a^{16} (b^{- 29} b^{2}) c^{34} \cdot 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 a^{16} b^{- 29 + 2} c^{34} \cdot 3$

Add $- 29$ and $2$ .

$15 a^{16} b^{- 27} c^{34} \cdot 3$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$15 a^{16} \frac{1}{b^{27}} c^{34} \cdot 3$

Step 5

Multiply $15 a^{16} \frac{1}{b^{27}}$ .

Combine $15$ and $\frac{1}{b^{27}}$ .

$a^{16} \frac{15}{b^{27}} c^{34} \cdot 3$

Combine $a^{16}$ and $\frac{15}{b^{27}}$ .

$\frac{a^{16} \cdot 15}{b^{27}} c^{34} \cdot 3$

Step 6

Move $15$ to the left of $a^{16}$ .

$\frac{15 \cdot a^{16}}{b^{27}} c^{34} \cdot 3$

Step 7

Combine $\frac{15 a^{16}}{b^{27}}$ and $c^{34}$ .

$\frac{15 a^{16} c^{34}}{b^{27}} \cdot 3$

Step 8

Multiply $\frac{15 a^{16} c^{34}}{b^{27}} \cdot 3$ .

Combine $\frac{15 a^{16} c^{34}}{b^{27}}$ and $3$ .

$\frac{15 a^{16} c^{34} \cdot 3}{b^{27}}$

Multiply $3$ by $15$ .

$\frac{45 a^{16} c^{34}}{b^{27}}$