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Popular >

simplify (T10^r)(610^5)

Solution

simplify

(T \cdot 1 0^{r}) (6 \cdot 1 0^{5})

Solution

3 \cdot 2^{r + 6} \cdot 5^{r + 5} T

Solution steps

(T \cdot 1 0^{r}) (6 \cdot 1 0^{5})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{r} \cdot 1 0^{5} = 1 0^{r + 5}

= T \cdot 6 \cdot 1 0^{r + 5}

Factor integer

6 = 2 \cdot 3

= T \cdot 2 \cdot 3 \cdot 1 0^{r + 5}

Factor integer

10 = 2 \cdot 5

= T \cdot 2 \cdot 3 (2 \cdot 5)^{r + 5}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{r + 5} = 2^{r + 5} \cdot 5^{r + 5}

= T \cdot 2 \cdot 3 \cdot 2^{r + 5} \cdot 5^{r + 5}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{r + 5} = 2^{1 + r + 5}

= T \cdot 3 \cdot 2^{1 + r + 5} \cdot 5^{r + 5}

Simplify

1 + r + 5 : r + 6

= 3 \cdot 2^{r + 6} \cdot 5^{r + 5} T

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Frequently Asked Questions (FAQ)

What is (T*10^r)(6*10^5) ?
The solution to (T*10^r)(6*10^5) is 3*2^{r+6}*5^{r+5}T