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ANEK [815]
2 years ago
15

Using the laws of indices simplify 625^3/8 ×5^1/2÷ 25​

Mathematics
1 answer:
Oxana [17]2 years ago
5 0

Answer:

1

Step-by-step explanation:

\huge {625}^{ \frac{3}{8} }  \times  {5}^{ \frac{1}{2} }  \div 25 \\  \\ =  \huge {( {5}^{4})}^{ \frac{3}{8} }  \times  {5}^{ \frac{1}{2} }  \div  {5}^{2}  \\  \\  =   \huge{5}^{ \cancel4 \times  \frac{3}{ \cancel8 \:  \:  \red{ \bold 2}} }  \times  {5}^{ \frac{1}{2} }  \div  {5}^{2}  \\  \\   \huge=  {5}^{ \frac{3}{2} }  \times  {5}^{ \frac{1}{2} }  \div  {5}^{2}  \\  \\ \huge=  {5}^{ \frac{3}{2}  + \frac{1}{2}}  \div  {5}^{2}  \\ \\ \huge=  {5}^{ \frac{4}{2}  }  \div  {5}^{2}  \\ \\ \huge=  {5}^{ 2  }  \div  {5}^{2}  \\  \\   \huge=  {5}^{ 2  - 2 }  \\  \\   \huge=  {5}^{ 0 }  \\  \\   \huge=  1

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