Question

simplify 3 power 5 x 10 power 5 multiply 25 by 5 power 7 multiply 6 power 7​

Answer 1

$\boxed{\dfrac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}=1}$

Step-by-step explanation:

Now, $\dfrac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$

• Hint: Express $10=2\times 5$ and use the formula $(a\times b)^{m}=a^{m}\times b^{m}$. Do the same for $6=2\times 3$

• Hint: Also, write $25=5\times 5=5^{2}$

$=\dfrac{3^{5}\times (2\times 5)^{5}\times (5\times 5)}{5^{7}\times (2\times 3)^{5}}$

$=\dfrac{3^{5}\times 2^{5}\times 5^{5}\times 5^{2}}{5^{7}\times 2^{5}\times 3^{5}}$

• Hint: Now we rearrange the terms to use the formulas $a^{m}\times a^{n}=a^{m+n}$ and $\dfrac{a^{m}}{a^{n}}=a^{m-n}$

$=\dfrac{2^{5}\times 3^{5}\times 5^{5}\times 5^{2}}{2^{5}\times 3^{5}\times 5^{7}}$

$=2^{5-5}\times 3^{5-5}\times 5^{5+2-7}$

$=2^{0}\times 3^{0}\times 5^{0}$

• Hint: We must know that the power $0$ for any non-zero number gives $1$, that is $a^{0}=1$, where $a\neq 0$

$=1\times 1\times 1$

$=1$

NOTE:

We can also find the simplified form by expanding the terms of the given fraction.

Answer 2

Answer:

The solution of the given expression is 1.

Step-by-step explanation:

Given: $\frac{3^5\times10^5\times25}{5^7\times6^5}$

We have to solve the above expression.

• As we know multiplication is a method to get the product by multiplying two or more values.
• Multiplication is denoted by the symbol(x).

Following are some properties of multiplication:

1. Closure property of multiplication
2. Commutative property of multiplication
3. Associative property of multiplication
4. Distributive property of multiplication over addition
5. Identity property of multiplication
6. Zero property of multiplication

We are solving in the following way:

We have,

$\frac{3^5\times10^5\times25}{5^7\times6^5}$

$=>\frac{243\times100000\times25}{78125\times7776} \\\\=>\frac{607500000}{607500000} \\\\=>1$

Hence, we get the solution is 1.